Assignments are quest-like activities that have various rewards. Always have one in progress, because you can only have on construction active at one time. Build things as soon as they are ready. Use the assignments as a guide to decide what to build next.
Attacking
Send out as many cheap units as possible at the start while continuing to push your opponent. Resource generation will be low at the start of a match. Your opponent will have greater difficulty fighting back after you are at an advantage. In campaign levels, you can preview what types of units the enemy has starting a battle. Red units are strong against Infantry. Green units are strong against Recon. Blue units are strong against Tanks. White units are strong against Air. Wait at the start of a match until your opponent deploys their first unit. Then deploy a type of your own that is strong against that type. Continue doing this after each turn. You will eventually be able to push in. After you reach level four or five of resource generation you should be able to clear it.
Chests
You can open a free chest in the officer's club every few hours for a chance to get a new unit, worth one or two stars. You will require units from each manufacturer to keep your army flexible. Complete campaigns levels to earn campaign keys. Ten of them are required to open a campaign chest, which contain untits that are worth up to three stars.
Research
Always have some sort of research queued. Researching new abilities will grant passive bonuses to all units and are always in effect. Bonuses obtained through research includes critical chance bonuses, ability improvements, and others.